A Hybrid Finite Element—Pseudospectral Approach for Simulating Nonlinear Pollutant Transport in Watercourses

This paper presents a novel hybrid numerical scheme that combines the Finite Element Method (FEM) and Pseudospectral Methods to simulate he nonlinear transport of pollutants in water environments. The mathematical model is based on a convection-diffusion-reaction equation coupled with a stationary incompressible Navier-Stokes velocity eld. By leveraging the geometric exibility of FEM and the high spatial resolution of spectral techniques, the proposed method offers improved accuracy and stability, even under limited regularity of the solution. Numerical simulations are conducted to evaluate the influence of key physical parameters such as the Reynolds number and reaction nonlinearity. The results highlight the robustness of the method and provide insights into pollutant dynamics in environmental flow scenarios.